Signal Analysis In The Ambiguity Domain

Abstract

Time-Frequency Distributions (TFDs) are accounted to be one of the powerful tools for analysis of time-varying signals. Although a variety of TFDs have been proposed, most of their designs were targeted towards obtaining good visualization and limited work is available for characterization applications. In this work, the characteristics of the ambiguity domain (AD) is suitably exploited to obtain a novel automated analysis scheme that preserves the inherent TF connection during Non-Stationary (NS) signal processing. Following this, an energy-based discriminative set of feature vectors for facilitating efficient characterization of the given time-varying input has been proposed. This scheme is motivated by the fact that, although, the interfering (or cross-) terms plague the representation, they carry important signal interaction information, which could be investigated for usability for time-varying signal analysis. Once having assessed the suitability of this domain for NS signal analysis, a new formulation for obtaining AD transformation is introduced. The number theory concepts, specifically the even-ordered Ramanujan Sums (RS) are used to obtain the proposed transform function. A detailed investigation and comparison to the classical approach, on this novel class of functions reveals the many benefits of the RS-modified AD functions: inherent sparsity in representation, dimensionality reduction, and robustness to noise. The next contribution in this work, is the proposal of kernel modifications in AD for obtaining high resolution (and good time localization) distribution. This is motivated by the existing trade-off between TF resolution and interfering term reduction in TF distributions. Here, certain variants of TF kernels are proposed in the AD. In addition, kernels that are derived from the concept of learning machines are introduced for discriminative characterization of NS signals. Following this, two novel AD-based schemes for neurological disorder discrimination using gait and pathological speech detection are introduced. The performance evaluation of these AD-based schemes, using a linear classifier, resulted in a maximum overall classification accuracy of 93.1% and 97.5% for gait and pathological speech applications respectively. The accuracies were obtained after a rigorous leave-one-out technique validation strategy.These results further confirm the potential of the proposed schemes for efficient information extraction for real-life signals.